Okay, we all know that someone with a wild card team ability can switch team abilities once per action. I was wondering if free actions count.

For example, suppose I'm using Veteran Doctor Doom (who is a wild card with running shot, two-arrows, and energy explosion), several Veteran U-Men (for enhancement), rookie Sinestro (with the Green Lantern team ability), and Veteran Ultimates Black Widow.

I give Doctor Doom a power action so that he can use running shot. For this action, I let Doctor Doom mimic the GL team ability so that he can carry more than one of the U-Men with him. After Dr Doom finishes his movement, I give him a free action to make a ranged combat action. Since this is a new action, can I then change his team ability to the Ultimates so that his ranged combat action can target people using Stealth?

Nope. The move and then attack of RS is all one action. If you copied the GL you couldn't change in the middle of it to pick up Ultimates.

Just move your U-men before

Right. Move your U-men with R Sinestro, then drop Doomsie in among them and fire.